On a frost free fridge, the compressor motor and the evaporator fan in the freezer compartment will come on and go off simultaneously.
So, if the evaporator fan is running, and you can hear a fan and feel a breeze in the freezer compartment, but the compressor isn't on, then it's a problem with the compressor, most likely the start relay isn't working.
If neither the evaporator fan nor the compressor are running, most likely neither one is getting power, and that's normally due to the defrost thermostat being stuck in defrost mode. If you've advanced the defrost timer so that you're out of defrost mode, then the only likely remaining cause would be the fridge thermostat (the "cold control") in the console of your fridge that tells the compressor when to come on based on the temperature in the fresh food compartment.
I'd turn that cold control up higher to see if the fridge comes on.
Also, check the dumb stuff. Check to see that the fridge light is going off when you close the fridge door. Check to see that you've got a good seal all the way around both door gaskets.